17050
J. Phys. Chem. 1996, 100, 17050-17058
Electrochemical Rectification at a Monolayer-Modified Electrode Kent S. Alleman,† Kara Weber,‡ and Stephen E. Creager*,‡ Department of Chemistry, Indiana UniVersity, Bloomington, Indiana 47405, and Department of Chemistry, Clemson UniVersity, Clemson, South Carolina 29634 ReceiVed: July 22, 1996X
An electrochemical current rectifier based on a ferrocene-monolayer-modified electrode in contact with an electrolyte solution containing sodium hexacyanoferrate(II) (sodium ferrocyanide) was constructed and evaluated. Rectification was accomplished via mediated ferrocyanide oxidation by electrogenerated ferricenium in monolayers of (10-mercapto-N-decyl)ferrocenecarboxamide with dodecanethiol and (7-mercapto-N-heptyl)ferrocenecarboxamide with nonanethiol on gold electrodes. The reverse reaction of ferricyanide reduction by immobilized ferrocene is thermodynamically disfavored, thereby providing the basis for rectification. A model proposed to describe the rectification process is reminiscent of earlier treatments of electron-transfer mediation at electrodes modified with redox polymers, with the important difference that, in the present system, long-range electron transfer across the monolayer replaces electron hopping through the polymer layer as a possible rate-limiting step. Steady-state current-voltage curves corresponding to mediated ferrocyanide oxidation were recorded and analyzed using the proposed model to give values for k0, the standard rate constant for electrochemical oxidation/reduction of immobilized ferrocene groups, and kcross, the rate constant for reaction of ferricenium ions in the monolayer with ferrocyanide ions in solution. Mean k0 values of 2700 ( 1000 s-1 for the (10-mercapto-N-decyl)ferrocenecarboxamide/dodecanethiol system and 90 000 ( 60 000 s-1 for the (7-mercapto-N-heptyl)ferrocenecarboxamide/nonanethiol system obtained by analysis of steady-state current-voltage data are to be compared with values of 1400 and 51 000 s-1 for the same systems obtained by the fast-scan cyclic voltammetry method. The kcross value of 1.1 × 108 M-1 s-1 obtained from analysis of steady-state current-voltage data for the (10-mercapto-N-decyl)ferrocenecarboxamide/dodecanethiol system is in good agreement with a value calculated using the Marcus expression with literature values for the electron self-exchange rate constants for ferrocene/ferricenium and ferrocyanide/ferricyanide, indicating that the reactivity of ferricenium ions in the monolayer is similar to that expected for ferricenium in free solution.
Introduction
SCHEME 1
Strategies for modifying electrode surfaces to control electrochemical reactivity via immobilized reagents have become highly developed,1 and modified electrodes have been used in electroanalysis,2 electrosynthesis,3 and other applications. One intriguing reaction promoted by chemically-modified electrodes is that of redox mediation. In this reaction, immobilized redox agents near an electrode surface are oxidized/reduced by the electrode. These agents then serve to oxidize/reduce other redox agents, usually in solution, for which the direct oxidation/ reduction at the electrode surface is inhibited, either because of intrinsically slow heterogeneous kinetics or because close approach of the soluble redox agent to the electrode is prevented. Scheme 1 illustrates the redox mediation process in terms of energy level diagrams for an electrode, an electron donor in solution, and a mediator species immobilized on an electrode surface. This is a different type of electrochemical reactivity than one usually thinks about at electrodes, since the properties of the modifying layer can control the rate, the chemical specificity, and even the directionality of current flow. It is hoped that one day advanced, possibly molecular-scale, electronic materials and devices might be prepared that can control electron flow by molecular mechanisms to accomplish higherorder functions.4-9 One simple function of a molecular electronic device is current rectification, and many devices that accomplish this have †
Indiana University. Clemson University. X Abstract published in AdVance ACS Abstracts, September 15, 1996. ‡
S0022-3654(96)02193-4 CCC: $12.00
been prepared from electrodes modified with redox polymer films. (References 10-12 provide excellent reviews and entries to the extensive original literature on this subject.10-12) Scheme 2 (top) illustrates the manner in which a polymer-based electrochemical current rectifier might work. Redox sites in the polymer near the electrode surface are electrochemically oxidized and the oxidizing equivalents transported to regions not in direct contact with the electrode by “electron hopping” among redox sites in the polymer. Electron donors in solution with access to sites near the outer portion of the polymer can be oxidized by electron exchange with oxidized sites in the polymer. If the reverse reaction of electron acceptors in solution with reduced sites in the polymer is thermodynamically disfavored and/or kinetically slow, and if electron donors/ acceptors in solution are denied direct access to the electrode © 1996 American Chemical Society
Electrochemical Rectification SCHEME 2
surface, perhaps by electrostatic screening or size exclusion by the polymer, then the device will permit current flow in only one direction and will act as a current rectifier. The behavior of such layers has been extensively considered from the point of view of kinetic modeling, usually in terms of current-limiting processes associated with electron propagation through the film, mass transfer in both the film and the solution, and the rate of the electron exchange reaction.10-20 These models have been widely used to interpret current-voltage data, often for polymermodified rotating disk electrodes, to obtain parameters describing the various redox and transport processes occurring within the polymer films. Several factors can combine to limit the performance of polymer-based devices as electrochemical current rectifiers, including possible direct access of soluble redox molecules to the electrode, reaction of solutes with active sites in the polymer interior, and limitations on the magnitude of current flow that can be supported by electron hopping in the polymer layer. These factors can place strict limitations on the chemical systems that might be used to construct an electrochemical electronic device. Our interest in the behavior of redox-active monolayers on electrodes, and in particular our experience with ferrocene-containing alkanethiol-based self-assembled monolayers on gold,21-24 prompted us to consider whether such systems might be useful for constructing a monolayer-based rectifying device. Scheme 2 (bottom) illustrates how such a monolayer-based device might behave in relation to a polymerbased device. Direct oxidation of electroactive solutes is suppressed everywhere except at those sites where a redox-active molecule is present in the monolayer; at those sites, solutes can undergo electron exchange with the immobilized redox molecule, thereby promoting indirect, mediated oxidation of the solute. Suppression of the direct oxidation/reduction of redoxactive solutes is key to the operation of such a device, and it has been demonstrated at alkanethiolate-coated electrodes in several laboratories.25-28 The suppression is thought to reflect the excellent barrier properties of a well-ordered, defect-free monolayer in preventing close approach of solutes to the electrode surface. Redox molecules immobilized in such monolayers are also commonly observed to behave similarly
J. Phys. Chem., Vol. 100, No. 42, 1996 17051 to related species in solution,24,29-33 with the one significant difference that the electron exchange kinetics between the redox molecule and the electrode are controlled in part by the nature of the bridging group linking the redox molecule to the electrode.22,34-40 We hypothesized that an electrogenerated electron acceptor (ferricenium) in the monolayer should react with electron donors in solution in a manner similar to that expected for ferricenium in solution and that this reaction could be the basis for a monolayer-based electrochemical rectification device. This paper describes our initial efforts aimed at preparing and characterizing such a device. Mixed self-assembled monolayers of (10-mercapto-N-decyl)ferrocenecarboxamide with dodecanethiol and (7-mercapto-Nheptyl)ferrocenecarboxamide with nonanethiol were prepared on gold electrodes and studied by steady-state voltammetric methods in the presence of the hexacyanoferrate(II) ion (present as the sodium salt, and hereafter referred to as ferrocyanide), a common, readily available, well-behaved electron donor. The relative oxidation/reduction potentials for ferrocene and ferrocyanide are such that ferrocyanide oxidation by ferricenium is favored but ferricyanide reduction by ferrocene disfavored. This is just the situation desired to accomplish electrochemical current rectification, as illustrated in Scheme 1. Voltammetric data are presented which demonstrate current rectification and suggest that rectification is probably due to mediated ferrocyanide oxidation by ferricenium. A model is proposed for the twostep mediation process in terms of microscopic rate parameters for each of the individual steps. Redox mediation at monolayercoated electrodes has been previously demonstrated;41-44 however, the emphasis on quantitative analysis in terms of microscopic rate parameters for the individual electron-transfer steps, as has been achieved for polymer-based systems, is unique to the present work with monolayers. One such rate parameter is k0, the rate constant for oxidation/reduction of ferrocene groups in the monolayer, and another is kcross, the rate constant for reaction of ferricenium in the monolayer with ferrocyanide in solution. Values for these rate constants obtained from analysis of steady-state current-voltage curves are found to be in good agreement with values obtained by independent measurement using fast-scan cyclic voltammetry, and also with values calculated from tabulated electron self-exchange rate constants using expressions from the Marcus theory of electron transfer. Experimental Section Acetic acid, sodium acetate, sodium perchlorate, sodium ferrocyanide, nonanethiol, dodecanethiol, and absolute ethanol were obtained as reagent-grade chemicals from commercial suppliers and used as received. Water for preparing electrolyte solutions was purified using a Barnstead Nanopure system. The electroactive alkanethiol derivatives (10-mercapto-N-decyl)ferrocenecarboxamide (Fe(C5H5)(C5H4)CONH(CH2)10SH) and (7-mercapto-N-heptyl)ferrocenecarboxamide (Fe(C5H5)(C5H4)CONH(CH2)7SH) were available from another project. They were prepared by amidation of ferrocene with the appropriate ω-bromoalkyl isocyanate, followed by conversion of bromide to thiol using thiourea. Details of the syntheses, including methods used for product purification and characterization, are given elsewhere.45 Gold disk electrodes were constructed by sealing lengths of annealed gold wire (1 mm diameter, 99.9%, Alfa) in epoxy (Shell EPON Resin 825, from Miller-Stephenson Chemical Co.) cross-linked using 1,3-phenylenediamine (Aldrich).46 Electrodes were pretreated by polishing to visual smoothness with progressively finer grades of alumina (5, 1, 0.3, and 0.05 µm), followed by sonication in soapy water for 8 min and twice in distilled,
17052 J. Phys. Chem., Vol. 100, No. 42, 1996 deionized water for 8 min, etching in dilute aqua regia (1:3:4 HNO3:HCl:H2O) for 2 min, and rinsing with water and ethanol. Monolayers were formed by immediate immersion of the treated electrodes in the coating solutions.47 Coating solutions were 1 mM total thiol concentration in ethanol, and coating times were approximately 19-24 h. To prepare monolayers containing ferrocene groups, coating solutions in ratios between 95:5 and 90:10 alkanethiol-to-ferrocenylalkanethiol were used. This was done to keep ferrocene surface coverages less than 1 × 10-11 mol cm-2 (corresponding to approximately 2% of the coverage expected for a full monolayer of ferrocenylalkanethiol).23 Slow-scan cyclic voltammograms and steady-state currentvoltage curves were acquired using a EG&G PAR Model 362 scanning potentiostat and an X-Y recorder. The electrolyte solution was 0.1 M NaClO4 in distilled deionized water, buffered at pH 5 with 0.18 M/0.10 M sodium acetate/acetic acid. Threeneck round-bottom or pear-shaped flasks were used as cells in the standard three-electrode configuration (working, reference, and auxiliary) with a solution volume between 5 and 50 mL. In most cases, sodium ferrocyanide solutions were prepared by adding an appropriate amount of dry solid directly to the electrochemical cell. Exceptions were when very low concentrations of ferrocyanide were needed; in such cases, dilute solutions were prepared, of which a small volume was added to the cell solution to achieve the desired concentration. Solutions containing ferrocyanide become oxidized over time (presumably by air), so fresh solutions were prepared for each experiment. A Ag/AgCl/saturated KCl reference electrode isolated from the main cell via an electrolyte-filled porous glass isolation tube was used. All cell solutions were sparged with nitrogen gas for at least 10 min prior to any measurements. In most cases, voltammograms were acquired in electrolyte before and after mediation currents were recorded. Voltammograms were recorded at relatively rapid scan rates (usually 0.5 V s-1) and were subsequently digitized with the aid of a flatbed digital scanner using Photoshop 2.5 (Adobe) and UnScanit (Silk Scientific) software to convert the scanned image into an ASCII text file of current/potential data points. These data were subsequently imported into a standard plotting package (SigmaPlot 2.0) for further processing and plotting. Currents were measured from an extrapolated base line assuming that the background current was constant at all potentials. Coverages of electroactive species were determined from peak areas calculated by UnScanit on voltammograms acquired in the absence of ferrocyanide. Fast-scan cyclic voltammetry was performed as described previously22 in aqueous 1.0 M perchloric acid. Rate constants were obtained from fits of peak potential vs log(scan rate) curves obtained from voltammograms acquired over a sweep rate range from 1 to 10 000 V s-1. Results and Discussion Qualitative Behavior. Figure 1 presents a series of cyclic voltammograms that qualitatively illustrate how a rationallydesigned molecular monolayer on an electrode surface can serve as a current rectification device. The bottom voltammogram was obtained at a bare gold electrode in a dilute solution of sodium ferrocyanide; it is included to illustrate the redox potential (E°′ ) +0.24 V) and the voltammetric behavior of ferrocyanide at an unmodified electrode. The voltammogram second from the bottom was obtained at an electrode coated with a mixed monolayer of (10-mercapto-N-decyl)ferrocenecarboxamide and dodecanethiol (FcCONH(CH2)10SH/H(CH2)12SH) in a solution containing no ferrocyanide. Rapid and chemically reversible oxidation/reduction of immobilized ferrocene groups
Alleman et al.
Figure 1. Cyclic voltammetry of modified electrodes showing current rectification via mediated electron transfer. Scan rate ) 0.5 V s-1, all solutions contain 0.1 M NaClO4, 0.1 M acetic acid, and 0.18 M sodium acetate, pH ) 5. (Bottom) Bare gold, solution contains 4.0 mM sodium ferrocyanide. (Second from bottom) Electrode coated with (10mercapto-N-decyl)ferrocenecarboxamide/dodecanethiol monolayer (ΓFc ) 5 × 10-12 mol cm-2); solution contains no ferrocyanide. (Third from bottom) Electrode coated with dodecanethiol only; solution contains 50 µM each of sodium ferrocyanide and sodium ferricyanide. (Top) Electrode coated with (10-mercapto-N-decyl)ferrocenecarboxamide/dodecanethiol monolayer (ΓFc ) 5 × 10-12 mol cm-2) and studied in solution containing 50 µM each of sodium ferrocyanide and sodium ferricyanide.
is indicated by the symmetric peaks at positive potentials (E°′ ) +0.55 V). The third voltammogram was obtained at an electrode coated with dodecanethiol alone (no ferrocene) in a solution containing 50 µM each of sodium ferrocyanide and sodium ferricyanide. The absence of voltammetric features corresponding to ferrocyanide oxidation/ferricyanide reduction reflects the excellent barrier properties of the dodecanethiolate monolayer. At the top of Figure 1 is a voltammogram obtained at the same ferrocene-containing monolayer-coated electrode used earlier, but now in contact with a solution containing sodium ferrocyanide and ferricyanide. The large anodic peak near + 0.5 V undoubtedly corresponds to ferrocyanide oxidation being mediated by ferrocene groups in the monolayer. Significantly, no cathodic peak corresponding to ferricyanide reduction is present on the return scan. (The small peak near +0.55 V probably corresponds to reduction of ferricenium in the monolayer and not to reduction of ferricyanide in solution.) This behavior corresponds formally to current rectification; i.e., current is made to pass in the forward direction but not the backward direction. The absence of a cathodic peak for ferricyanide reduction, and the fact that the anodic peak is shifted positive of that for
Electrochemical Rectification
J. Phys. Chem., Vol. 100, No. 42, 1996 17053 SCHEME 3
Figure 2. Cyclic voltammetry of a (10-mercapto-N-decyl)ferrocenecarboxamide/dodecanethiol-coated gold electrode (ΓFc ) 6 × 10-12 mol cm-2) in solutions containing the indicated concentrations of sodium ferrocyanide. Other conditions are the same as those in Figure 1.
ferrocyanide oxidation at an unmodified electrode but still negative of that for ferrocene oxidation in the monolayer, both suggest strongly that ferrocyanide oxidation is occurring in a mediated fashion via reaction of electrogenerated ferricenium with ferrocyanide. The relative formal potentials for the immobilized ferrocene and the dissolved ferrocyanide suggest that this will be so; i.e., ferricenium should be a strong enough oxidant to oxidize ferrocyanide (the forward mediation reaction will be thermodynamically favorable), but ferrocene should not be a strong enough reductant to reduce ferricyanide (the reverse mediation reaction will be thermodynamically unfavorable). Figure 2 presents a series of voltammograms that further support this hypothesis. These voltammograms were obtained under conditions similar to those in Figure 1 (top), except that the concentration of ferrocyanide in solution was systematically varied between zero and 10-4 M. The larger anodic peak clearly grows in as a shoulder on the ferrocene oxidation peak, and its magnitude clearly correlates with the concentration of added ferrocyanide, as expected for a mediated process. Modeling and Simulations. Having hypothesized that current rectification occurs at the monolayer-modified electrode via electron-transfer mediation, it is useful to devise a simple physical model for the phenomenon and treat it mathematically. Scheme 3 presents a simplistic model for electrochemical oxidation of an electron donor, D, by an immobilized redox mediator, O/R. The three critical rate parameters in this model are the heterogeneous first-order rate constants for reduction and oxidation of the immobilized mediator (kred and kox, units of s-1) and the homogeneous second-order rate constant for reaction of oxidized mediator with electron donor (kcross, units
of M-1 s-1). To first order, the magnitudes of kred and kox will depend on the potential applied to the electrode and the standard rate constant k0 for oxidation/reduction of the immobilized mediator and that of kcross on the formal potentials and electron self-exchange rate constants for the mediator and the donor/ acceptor redox couples. The mediation reaction is assumed to be thermodynamically favorable and the back-reaction sufficiently unfavorable and/or slow that it can be ignored. (This assumption is justified since the formal potential for ferrocene oxidation is substantially more positive than that for ferrocyanide oxidation.) It is also assumed that the donor concentration at the electrode surface is relatively unperturbed by the mediation reaction; i.e., there is relatively little concentration polarization of donor associated with the mediation reaction. (Experimental evidence for this condition is obtained by variation of the potential sweep rate; currents that are sweep-rate independent are indicative of minimal concentration polarization.) This is true only when the current is small relative to the diffusionlimited value, which in turn is true only at the very foot of voltammetric waves such as those in Figures 1 and 2. For this reason, and because in this potential region the degree of conversion from reduced to oxidized mediator is very small, we have restricted our quantitative analyses to currents near the foot of the voltammetric waves. Of course, these restrictions will not be met under all circumstances, and a more rigorous analysis, particularly one that accounts for the mediation backreaction, concentration polarization in solution, and a significant degree of conversion of the mediator, is desired. Even so, the relatively simple treatment described below has provided important insights into redox mediation at monolayer-coated electrode and has proved valuable.
net rate )
i ) kcrossCDΓO nFA
(1)
The overall reaction rate in the model above is the rate of acceptor production via reaction of donor with oxidized mediator. This can be expressed by a conventional rate law, as given in eq 1. The terms CD and ΓO represent respectively the concentration of donor in solution (moles per unit volume) and the concentration of oxidized mediator at the electrode surface (moles per unit area). The current is a direct measure of the reaction rate, provided that it is normalized for the number of electrons in the reaction, n, the Faraday constant, F, and the area of the electrode, A. Units for the net rate are moles per unit area per unit time, i.e., mol cm-2 s-1.
17054 J. Phys. Chem., Vol. 100, No. 42, 1996
∂ΓO/∂t ) 0 ) (koxΓR) - (kredΓO) - (kcrossΓOCD)
Alleman et al.
(2)
It is useful to make a steady-state assumption for the oxidized mediator, such that the rate of change of ΓO with time, ∂ΓO/∂t, is set equal to zero. The term ∂ΓO/∂t is also given by the difference between the rate of generation (by electrochemical oxidation of reduced mediator) and the rate of consumption (by electrochemical reduction and by reaction with donor) of the oxidized mediator. Each of these processes can be described by a conventional rate law, as expressed in eq 2. Solving eq 2 for ΓO, substituting into eq 1, and making the final simplifying assumption that the concentration of reduced mediator, ΓR, is equal to the total concentration of mediator, ΓT (equivalent to assuming ΓO , ΓR, since ΓT ) ΓO + ΓR), yield the expression for the current given in eq 3.
kcrosskoxCD i ) nFAΓT kred + (kcrossCD)
(3)
The form of eq 3 suggests two limiting cases, one in which kred . kcrossCD and another in which kred , kcrossCD. Mathematical expressions of these two limiting cases, which correspond to kinetics regimes in which the either the reaction of oxidized mediator with donor (case 1) or the electrochemical generation of the oxidized mediator (case 2) limits the overall rate, are given in eqs 4 and 5.
case 1:
kox i ) kcrossCD nFAΓT kred
(4)
case 2:
i/nFAΓT ) kox
(5)
It is useful at this juncture to adopt a model describing the dependence of the electrochemical rate constants, kox and kred, on the applied potential. The relatively simple formalism of Butler and Volmer48 for describing activated electron transfer at electrodes is well-suited and is used in the following treatment. The situation is particularly simple for case 1, since the electrochemical rate constants are present as a ratio that is formally equal to the equilibrium constant for oxidation/ reduction of the mediator at the applied potential. This reflects the fact that in this case the mediator electrode reaction is in a preequilibrium state, with the overall rate being governed by the (relatively slow) reaction of oxidized mediator with donor. In case 2 the opposite is true; i.e., the overall rate is limited by the rate of electrooxidative production of oxidized mediator, which is subsequently consumed by (relatively rapid) reaction with donor. Equations 6 and 7 are mathematical expressions of these two cases with potential included explicitly and the term nFAΓT replaced by Q, the charge associated with complete oxidation/reduction of all the mediator present on the electrode surface. (Note that the E° value in these equations is that of the mediator.) For case 2, note that substituting for kox introduces two new parameters, the standard electrochemical rate constant, k0, and the cathodic electrochemical transfer coefficient, R.
case 1:
nF i ) kcrossCD exp (E - E°) Q RT
case 2:
(1 - R)nF i ) k0 exp (E - E°) Q RT
[
[
]
(6)
]
(7)
Implications of this treatment for the interpretation of current-voltage data are particularly evident in eqs 6 and 7. For example, in case 1 systems, currents are predicted to scale
Figure 3. Simulated current Vs potential curves illustrating the effect of systematic variation of k0. Calculations were carried out using eq 3 with the following input parameters: kcross ) 1 × 1011 cm3 mol-1 s-1, CD ) 0.3 M, ΓT ) 1 × 10-11 mol cm-2, E°mediator ) 0.55 V, A ) 0.0105 cm2, T ) 298 K, R ) 0.5, n ) 1. Input values for k0 were 10 000, 5000, 2000, and 1000 s-1 from top to bottom.
with CD and kcross but to be independent of k0 for the mediator. Similarly, for case 2 systems, currents should be independent of both CD and kcross but should depend strongly on k0 for the mediator. Semilog plots of current Vs potential are also expected to exhibit different slopes, depending on which case applies, suggesting that such a plotting format will be useful. A potentially confusing issue is that a given current-voltage scan can change from case 1 to case 2 behavior in different potential regions. This happens because the magnitude of kred depends on potential. Similarly, a given system can change from one case to another for different concentrations of donor. This interdependence among experimental parameters is seen most clearly in current-voltage simulations using the above equations. Figures 3 and 4 present two sets of simulated current-voltage curves, one comprising a systematic variation of k0 and the other a systematic variation in CD, to illustrate this point. Input parameters were selected to illustrate a transition from case 1 to case 2, and at least one curve in each set shows this transition clearly. The region with the higher slope in the semilog current Vs potential curves corresponds to case 1 behavior and that with the lower slope to case 2 behavior. Figure 3 shows that currents become less dependent on the mediator k0 value when case 1 behavior applies (bottom left side of the figure), and Figure 4 shows that currents become less dependent on CD when case 2 behavior applies (top right side of the figure). These insights will prove valuable in deciding which case (if either) is appropriate for analyzing experimental data sets.
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J. Phys. Chem., Vol. 100, No. 42, 1996 17055
Figure 5. Plots of currents Vs sodium ferrocyanide concentration at various potentials Vs Ag/AgCl at a (10-mercapto-N-decyl)ferrocenecarboxamide/dodecanethiol-coated gold electrode.
Figure 4. Simulated current Vs potential curves illustrating the effect of systematic variation of CD. Calculations were carried out as in Figure 3, except that k0 was fixed at 10 000 s-1 and CD values were (from top to bottom) 0.3, 0.03, 0.003, and 0.0003 M.
It is important to note that the above treatment is more than simply a limiting case of earlier treatments of redox mediation at polymer-modified electrodes. Electron transfer at the electrode-film interface in polymer-modified electrodes is almost always assumed to be rapid, whereas, in the present treatment, electron transfer at the electrode-film interface is treated explicitly. Taking the limiting case in earlier treatments of rapid electron hopping and slow mass transfer through the film, such that the mediation reaction occurs at the film-solution interface (i.e., case RS in the Andrieux-Saveant treatment10 and case LS in the Hillman-Albery treatment17), yields a solution similar to the present case I, with the important difference being that, in the present case, the potential dependence of the mediator concentration is explicitly considered. The analogue of the present case 2, in which the potential-dependent reaction of the mediator with the electrode is rate-limiting, has not (to our knowledge) been previously treated. Quantitative Data Analysis. Returning to the (10-mercaptoN-decyl)ferrocenecarboxamide/dodecanethiol/ferrocyanide system in Figures 1 and 2, the model above (in particular eqs 6 and 7) suggests that examining the dependence of current on donor concentration will be useful in deciding whether a system is in the case 1 or case 2 regime. Figure 5 gives the results of such an experiment, presented as a series of plots (at different potentials) of steady-state current Vs ferrocyanide concentration. It was our hope that, by making CD very large, the product kcrossCD could be made much larger than kred at all potentials of interest, thereby ensuring that the system corresponds to case 2 behavior at all potentials. At ferrocyanide concentrations near 0.3 M the current was found to be almost completely independent of ferrocyanide concentration at all potentials examined,
thereby indicating that case 2 applies. Current-voltage curves obtained at high ferrocyanide concentration and analyzed according to eq 7 should therefore yield values for R and k0 from the slope and the intercept at E°′ of semilog current Vs voltage plots. As the ferrocyanide concentration decreases, the current begins to also slowly decrease, as expected for a system undergoing a transition from case 2 to case 1. It follows that analysis of current-voltage curves obtained at low ferrocyanide concentration according to eq 6 should yield values for kcross from the intercept of semilog current Vs voltage plots. Figure 6 presents current-voltage data and semilog current Vs potential plots for the (10-mercapto-N-decyl)ferrocenecarboxamide/dodecanethiol/ferrocyanide system in both the case 1 and case 2 regimes. The top panel is an expanded view of current-voltage curves from the foot of voltammetric waves corresponding to ferrocyanide oxidation (concentration 0.3 M) at (A) a bare gold electrode, (B) a (10-mercapto-N-decyl)ferrocenecarboxamide/dodecanethiol-coated electrode, and (C) a dodecanethiol-coated electrode. The middle curve (B) corresponds to mediated ferrocyanide oxidation by electrogenerated ferricenium, and the other two are included as controls to illustrate the behavior without the modifying layer present (A) and without the ferrocene present (C). The middle panel is a semilog plot of curve B from the upper panel (after normalization of the current by Q); the slope of the best-fit line (22.6 V-1) to this curve yields a value of 0.43 for R, and the y-intercept at E° (in this case +0.52 V Vs Ag/AgCl) is 7.9, which corresponds to a k0 value of 2700 s-1 for oxidation/reduction of ferrocene groups in this monolayer. This experiment was repeated with six independently prepared electrodes with ferrocene coverages between 5 × 10-12 and 2 × 10-11 mol cm-2, studied in freshly prepared solutions, to establish error limits; a mean k0 value of 2700 ( 1000 s-1 (95% confidence limits) was obtained from these data. It is instructive to compare this k0 value obtained by a steadystate method involving assumptions about follow-up reaction rates to a value obtained independently by a more direct measurement. Fast-scan cyclic voltammetry is a measurement tool with the temporal resolution required to make such a measurement.22,36,37 Figure 7 presents the results of a fast-scan cyclic voltammetric study of ferrocene oxidation in monolayers at scan rates between 1 and 10 000 V s-1. The data given by the circles in Figure 7 correspond to a monolayer of (10mercapto-N-decyl)ferrocenecarboxamide with dodecanethiol;
17056 J. Phys. Chem., Vol. 100, No. 42, 1996
Alleman et al. rate); by fitting such a curve to predictions from theory using a previously described procedure,22 we obtain a value for k0 of 1400 s-1. Past experience with fitting fast-scan voltammetry data for similar monolayers suggests that this value is probably accurate to within approximately 10%. Factors that might contribute to the discrepancy between rate constants obtained using the steady-state and fast-scan voltammetry methods include ion-pairing between ferricenium and ferrocyanide and/ or ferricyanide, contributions to the steady-state current from direct ferrocyanide oxidation at defect sites in the monolayer, and possible steric screening of ferrocene sites within the monolayer. The role of a distribution in rate constants in each of the two methods may also be important. Overall, considering the differences between the two methods used to obtain the k0 values, we consider the agreement between them to be good. The bottom panel of Figure 6 is a semilog current Vs potential plot for ferrocyanide oxidation at a similar ferrocene-monolayercoated electrode in a solution containing 3 × 10-5 M of sodium ferrocyanide, 4 orders of magnitude less than in the upper panels. (We note that the particular monolayer used in this experiment exhibited a lower ferrocene coverage than the one used in the experiment in the middle panel; this is accounted for in the data analysis by normalizing the current, i, to the charge, Q, required to fully oxidize or reduce the monolayer.) The slope of the plot (36.7 V-1) is now quite close to the value predicted for case 1 in the above model (F/RT ) 38.9 V-1; see eq 6), strongly suggesting that the diminished ferrocyanide concentration has brought about a transition from case 2 to case 1 behavior. The y-intercept of 8.1 at E° for the mediator was analyzed via eq 6 to yield a kcross value of 1.1 × 108 M-1 s-1.
kcross = [k11k22K12f12]1/2 Figure 6. Current-voltage curves and semilog current Vs potential plots for the (10-mercapto-N-decyl)ferrocenecarboxamide/dodecanethiol/ ferrocyanide system. (Top) Expanded current-voltage curves from the foot of voltammetric waves corresponding to ferrocyanide oxidation (sodium ferrocyanide concentration 0.3 M) at (A) bare gold, (B) a (10mercapto-N-decyl)ferrocenecarboxamide/dodecanethiol-coated gold (ΓFc ) 1.5 × 10-11 mol cm-2), and (C) dodecanethiol-coated gold. (Middle) Curve B from top panel normalized to Q and plotted in semilog current Vs potential format. (Bottom) Semilog(normalized current) Vs potential curve for (10-mercapto-N-decyl)ferrocenecarboxamide/dodecanethiolcoated gold (ΓFc ) 6 × 10-12 mol cm-2) in solution containing 3 × 10-5 M sodium ferrocyanide.
Figure 7. Fast-scan cyclic voltammetry data, plotted as curves of peak potential Vs log(scan rate), for ferrocene oxidation in monolayers of (10-mercapto-N-decyl)ferrocenecarboxamide with dodecanethiol (circles) and (7-mercapto-N-heptyl)ferrocenecarboxamide with nonanethiol (squares).
those given by the squares correspond to a monolayer of (7mercapto-N-heptyl)ferrocenecarboxamide with nonanethiol and will be discussed further below. The data are presented as plots of peak potential (relative to the formal potential) Vs log(scan
(8)
A calculated value for kcross can be obtained via eq 8 from the Marcus theory of electron transfer.49-51 In this expression, k11 and k22 are the homogeneous electron self-exchange rate constants for the two redox couples involved in the reaction (ferrocene/ferricenium and ferro-/ferricyanide), K12 is the equilibrium constant for the cross-reaction (given by the Nernst equation using the formal potentials of the two redox couples), and f12 is a factor that under most conditions assumes a value near 1. Electron self-exchange rate constants are usually obtained from NMR and ESR line broadening data, and values have been reported for ferrocene/ferricenium (k11 ) (5-9) × 106 M-1 s-1 in CH3CN52-55) and ferrocyanide/ferricyanide (k22 ) (0.1-9) × 104 M-1 s-1 in H2O at various ionic strengths56). Using formal potentials of ferrocene and ferrocyanide measured under the conditions of our experiment (+0.55 and +0.24 V Vs Ag/AgCl, respectively), we readily calculate a K12 value of 1.75 × 105. Substituting these K12, k11, and k22 values into eq 8 yields a range for kcross of (0.3-3) × 108 M-1 s-1, which brackets quite nicely the value derived from the intercept on the plot at the bottom of Figure 6. The agreement between theory and experiment is good but approximate, given the uncertainties in both the measured and the calculated values. Even so, the agreement suggests fairly strongly that the reactivity of ferricenium in the monolayer with a ferrocyanide donor is not greatly different from that expected for ferricenium in solution. This is a significant finding, since it suggests that the accessibility of ferricenium groups in the monolayer for reaction with ferrocyanide in solution is not greatly different than what would be expected for the same reaction occurring in free solution. Figure 8 presents steady-state current-voltage curves presented in normal and semilog format for mediated ferrocyanide oxidation at a (7-mercapto-N-heptyl)ferrocenecarboxamide/
Electrochemical Rectification
J. Phys. Chem., Vol. 100, No. 42, 1996 17057 51 000 s-1. This is well within the range of values obtained by the steady-state method, although the value obtained by fastscan voltammetry is again on the low side. The agreement in this case is probably less significant than it might be since the range of values obtained from the steady-state method is fairly broad. Summary The present work demonstrates electrochemical rectification at an electrode coated with a redox-active monolayer film. Rectification is accomplished by electron-transfer mediation involving ferrocene groups immobilized in monolayers and ferrocyanide donors in solution. Steady-state current-voltage curves were interpreted using a model that includes rate constants for electrochemical oxidation/reduction of ferrocene groups in the monolayer and for the electron transfer crossreaction of electrogenerated ferricenium ion with ferrocyanide in solution as parameters. Rate constants obtained by using this model to analyze steady-state current-voltage curves corresponding to mediated ferrocyanide oxidation were in good agreement with values obtained by independent measurement using fast-scan voltammetry and with calculated values obtained from tabulated electron self-exchange rate constants for the ferrocene and ferrocyanide redox couples using expressions from the Marcus expression for electron transfer cross-reactions.
Figure 8. Current-voltage curves and semilog current Vs potential plots for the (7-mercapto-N-heptyl)ferrocenecarboxamide/nonanethiol/ ferrocyanide system. (Top) Expanded current-voltage curves from the foot of voltammetric waves corresponding to ferrocyanide oxidation (sodium ferrocyanide concentration 0.3 M) at (A) bare gold, (B) (7mercapto-N-heptyl)ferrocenecarboxamide/nonanethiol-coated gold (ΓFc ) 5 × 10-12 mol cm-2), and (C) nonanethiol-coated gold. (Bottom) Curve B from top panel and five independently measured curves from similar experiments, plotted in semilog current Vs potential format after normalization of the current by the charge for oxidation/reduction of ferrocene. Dotted lines show extrapolated least-squared-error regression fits to the experimental curves.
nonanethiol-coated gold electrode. The chain linking the ferrocene group to the electrode in this monolayer is substantially shorter than in the monolayer considered above, so it is expected that the rate constant for ferrocene oxidation/reduction will be greater. As in Figure 6, curve A in the top panel of Figure 8 was acquired at an uncoated electrode, curve B at a ferrocene-coated electrode, and curve C at a nonanethiol-coated electrode. One difference between Figures 6 and 8 is that the mediated current (B) and the background current (C) are more similar to one another for the short-chain system than for the long-chain system. This undoubtedly reflects the fact that the barrier properties of the nonanethiol monolayer are not as good as those of the dodecanethiol monolayer; ferrocyanide oxidation across the monolayer and/or at defect sites can occur more easily when the monolayer is thinner. This uncertainty in the relative contributions of mediated and nonmediated pathways for ferrocyanide oxidation is (we believe) reflected in the semilog current Vs potential plots in the bottom panel of Figure 8. Data for six different experiments are shown in the plot; all of the plots have similar slopes (average slope ) 24.3 V-1, which is in the correct range for case 2 behavior); however, the range of intercepts (10.6-12.2, corresponding to k0 values between 42 000 and 200 000 s-1 with a mean value of 90 000 ( 60 000 s-1, 95% confidence limits) is greater than was typical for the longer-chain monolayer. The fast-scan voltammetry data given by the squares in Figure 7 correspond to oxidation of ferrocene in a (7-mercapto-N-heptyl)ferrocenecarboxamide/nonanethiol monolayer, and the k0 value obtained by fitting these data is
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